Regularity of the Optimal Stopping Problem for Lévy Processes with Non-degenerate Diffusions
نویسندگان
چکیده
The value function of an optimal stopping problem for a process with Lévy jumps is known to be a generalized solution of a variational inequality. Assuming the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Lévy measure, this paper shows that the value function of problems on an unbounded domain with infinite activity jumps is W 2,1 p,loc . As a result, the smooth-fit property holds and the value function is C inside the continuation region.
منابع مشابه
On a class of optimal stopping problems for diffusions with discontinuous coefficients
In this paper we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows to apply this PDE method also in cases where the usual regularity assumptions on the coefficients and on the gain function are not satisfied. We apply this method to the optimal stopping of integral functionals with exponential discount of...
متن کاملOn the Optimal Stopping Time Problem for Degenerate Diffusions
In this paper we give a characterization of the optimal cost of a stopping time problem as the maximum solution of a variational inequality without coercivity. Some properties of continuity for the optimal cost are also given. Introduction. Summary of main results. This article develops the proofs of results obtained in Note [12]. A. Bensoussan and J. L. Lions [3] have introduced the variationa...
متن کاملFunctional Quantization Rate and Mean Regularity of Processes with an Application to Lévy Processes
We investigate the connections between the mean pathwise regularity of stochastic processes and their L(P)-functional quantization rates as random variables taking values in some L([0, T ], dt)-spaces (0 < p ≤ r). Our main tool is the Haar basis. We then emphasize that the derived functional quantization rate may be optimal (e.g., for Brownian motion or symmetric stable processes) so that the r...
متن کاملContributions to the Theory of Optimal Stopping for One – Dimensional Diffusions
Contributions to the Theory of Optimal Stopping for One–Dimensional Diffusions Savas Dayanik Advisor: Ioannis Karatzas We give a new characterization of excessive functions with respect to arbitrary one–dimensional regular diffusion processes, using the notion of concavity. We show that excessive functions are essentially concave functions, in some generalized sense, and vice–versa. This, in tu...
متن کاملConstruction of the Value Function and Optimal Rules in Optimal Stopping of One-dimensional Diffusions
A new approach to the solution of optimal stopping problems for one-dimensional diffusions is developed. It arises by imbedding the stochastic problem in a linear programming problem over a space of measures. Optimizing over a smaller class of stopping rules provides a lower bound on the value of the original problem. Then the weak duality of a restricted form of the dual linear program provide...
متن کامل